Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
715 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 715 conjugacy classes of subgroups — too many to draw. Only its 92 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×#272 | C2 | semidirect |
| 2. C2×#6235 | C2 | semidirect |
| 3. C2×C4⋊#272 | C2 | semidirect |
| 4. C22⋊C4×H(3,𝔽3) | C2 | semidirect |
| 5. #88542 | C2 | semidirect |
| 11. C22×#272 | C22 | semidirect |
| 12. C2×C4×H(3,𝔽3) | C22 | semidirect |
| 14. C2×#1084 | C22 | semidirect |
| 19. C32×C22⋊C4 | D3 | semidirect |
| 22. C22×H(3,𝔽3) | D4 | semidirect |
| 29. C2×#272 | D4 | semidirect |
| 39. C2×C32×C4 | C2×D3 | semidirect |
| 59. C22×C32 | D12 | semidirect |
| 70. H(3,𝔽3) | #120 | semidirect |
| 98. C22⋊C4 | #272 | semidirect |
| 121. C32 | #882 | semidirect |
| 130. C2×C4 | C2×#272 | semidirect |
| 148. C22 | C4⋊#272 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#272 | 2 |
| C2×#6235 | 2 |
| C2×C4⋊#272 | 2 |
| C22⋊C4×H(3,𝔽3) | 2 |
| #88542 | 2 |
| C3×#882 | 3 |